Wireless sensor networks (WSNs) are commonly employed for many applications including for environmental protection, structural monitoring and passive localization and tracking. A large number of inexpensive sensor nodes with low size, weight and power (SWAP) can be randomly distributed across an area of interest. These nodes operate as transceivers, communicating with one another in an ad-hoc manner, and can be at unknown locations. This is with the exception of a very small number of so-called anchor nodes, which can be at known locations. In commercial applications such as water quality monitoring as well as in military applications such as gunshot detection, an accurate knowledge of the location where an event occurs can be highly beneficial to the users of the system. In many applications, measured sensor data is meaningful only when the location of sensors is accurately known.
In general, localization techniques can be classified into range-based and direction-based approaches. Common range-based approaches are time of arrival (TOA), time difference of arrival (TDOA), and received signal strength (RSS). Direction-based approaches include direction of arrival (DOA) estimation techniques implemented by employing antenna arrays at each sensor. Large aperture array (LAA) localization algorithms jointly use direction and range-based information to localize a source by forming a single large aperture array of sensors.
Despite the prevalence of fading in practice, prior techniques do not address the Cramer-Rao lower bound (CRLB) for localization under fading environments. Although some prior techniques have considered fading environments for TOA measurements, CRLB for localization error under fading environments has not been addressed.
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The terms “first,” “second,” “third,” “fourth,” and the like in the description and in the claims, if any, are used for distinguishing between similar elements and not necessarily for describing a particular sequential or chronological order. It is to be understood that the terms so used are interchangeable under appropriate circumstances such that the embodiments described herein are, for example, capable of operation in sequences other than those illustrated or otherwise described herein. Furthermore, the terms “include,” and “have,” and any variations thereof, are intended to cover a non-exclusive inclusion, such that a process, method, system, article, device, or apparatus that comprises a list of elements is not necessarily limited to those elements, but may include other elements not expressly listed or inherent to such process, method, system, article, device, or apparatus.
The terms “left,” “right,” “front,” “back,” “top,” “bottom,” “over,” “under,” and the like in the description and in the claims, if any, are used for descriptive purposes and not necessarily for describing permanent relative positions. It is to be understood that the terms so used are interchangeable under appropriate circumstances such that the embodiments of the invention described herein are, for example, capable of operation in other orientations than those illustrated or otherwise described herein.
The terms “couple,” “coupled,” “couples,” “coupling,” and the like should be broadly understood and refer to connecting two or more elements or signals, electrically, mechanically or otherwise. Two or more electrical elements may be electrically coupled, but not mechanically or otherwise coupled; two or more mechanical elements may be mechanically coupled, but not electrically or otherwise coupled; two or more electrical elements may be mechanically coupled, but not electrically or otherwise coupled. Coupling (whether mechanical, electrical, or otherwise) may be for any length of time, e.g., permanent or semi-permanent or only for an instant.
“Electrical coupling” and the like should be broadly understood and include coupling involving any electrical signal, whether a power signal, a data signal, and/or other types or combinations of electrical signals. “Mechanical coupling” and the like should be broadly understood and include mechanical coupling of all types. The absence of the word “removably,” “removable,” and the like near the word “coupled,” and the like does not mean that the coupling, etc. in question is or is not removable.